Must one pay for a water hose accidentally broken in a government hospital? And was it sufficient to give its price as charity to one of the hospital workers?

You are not liable if your action was a normal use of the equipment; otherwise, you are liable for what you damaged and must pay it to the person responsible for the hospital. If that is not possible, then spend it on public utilities and charitable acts. The determination of normal use or transgression is to be referred to experts.